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The matrix associated with the discretization is symmetric positive definite and equal to the standard 7-point finite difference Poisson stencil away from embedded interfaces and boundaries.
Following a brief discussion of the mechanisms by which embedded interfaces can enhance the electronic and thermal transport properties, we focus on emerging routes to engineer the nanoscale grain and interfacial structures in bulk thermoelectric materials.
Oevermann, R. Klein, A Cartesian grid finite volume method for elliptic equations with variable coefficients and embedded interfaces, Journal of Computational Physics 219 (2006) 749–769] we use a minimization technique to determine the unknown coefficients of the double trilinear ansatz.
We present examples to demonstrate the effectiveness of the IAC grid generation algorithm for multiple embedded interfaces in a quadrilateral grid.
The issues involved in parallelization of the moving boundary flow solver are presented with emphasis on strong shocks interacting with embedded interfaces (solid fluid and solid solid) in a three-dimensional compressible flow framework.
The granular superconductivity behavior is observed only for fields normal to the embedded interfaces, whereas no relevant hysteresis in temperature or field is observed for fields applied parallel to them.
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One of them is developing a three-dimensional finite element with an embedded interface for analyzing the laminated composite structure.
It illustrates the presence of two leaching mechanisms: a fast one from the top coat surface and a slow one from an embedded interface.
Numerical examples, in which the proposed method is used to integrate the weak form of the Navier Stokes equations in an embedded interface method (EIM), are presented.
When the coefficients of an elliptic problem have jumps of several orders of magnitude across an embedded interface, many iterative solvers exhibit deteriorated convergence properties or a loss of efficiency and it is difficult to achieve high solution accuracies in the whole domain.
In this paper we present an asymptotic solution approach for the elliptic problem ∇⋅(β(x)∇u(x))="f(x) on a domain Ω="Ω+∪Ω− with piecewise constant coefficients β+, β− with β+≫β− and prescribed jump conditions at an embedded interface Γ separating the domains Ω+ and Ω−.
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